Question: Solve for $x$ and $y$ using elimination. ${-5x-3y = -26}$ ${3x+3y = 24}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-2x = -2$ $\dfrac{-2x}{{-2}} = \dfrac{-2}{{-2}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-5x-3y = -26}\thinspace$ to find $y$ ${-5}{(1)}{ - 3y = -26}$ $-5-3y = -26$ $-5{+5} - 3y = -26{+5}$ $-3y = -21$ $\dfrac{-3y}{{-3}} = \dfrac{-21}{{-3}}$ ${y = 7}$ You can also plug ${x = 1}$ into $\thinspace {3x+3y = 24}\thinspace$ and get the same answer for $y$ : ${3}{(1)}{ + 3y = 24}$ ${y = 7}$